Sequentially firing neurons confer flexible timing in neural pattern generators

Abstract

Neuronal networks exhibit a variety of complex spatiotemporal patterns that include sequential activity, synchrony, and wavelike dynamics. Inhibition is the primary means through which such patterns are implemented. This behavior is dependent on both the intrinsic dynamics of the individual neurons as well as the connectivity patterns. Many neural circuits consist of networks of smaller subcircuits (motifs) that are coupled together to form the larger system. In this paper, we consider a particularly simple motif, comprising purely inhibitory interactions, which generates sequential periodic dynamics. We first describe the dynamics of the single motif both for general balanced coupling (all cells receive the same number and strength of inputs) and then for a specific class of balanced networks: circulant systems. We couple these motifs together to form larger networks. We use the theory of weak coupling to derive phase models which, themselves, have a certain structure and symmetry. We show that this structure endows the coupled system with the ability to produce arbitrary timing relationships between symmetrically coupled motifs and that the phase relationships are robust over a wide range of frequencies. The theory is applicable to many other systems in biology and physics.